Stability of solutions to impulsive differential equations in critical cases

Об Устойчивости По Нелинейному Квазиоднородному Приближению Дифференциальных Уравнений С Импульсным Воздействием

“…В работе [12] обоснован принцип сведения для импульсных систем в некоторых частных случаях. В работе [13] исследованы аналоги некоторых классических критических случаев, общий способ построения функции Ляпунова для импульсных систем в критических случаях представлен в [14]. Важным вопросом для теории устойчивости критических положений равновесия импульсных систем является исследование устойчивости по квазиоднородному приближению.…”

New Conditions for the Exponential Stability of Nonlinear Differential Equations

“…The stability and robustness of pseudo-linear differential equations are considered, for example, in [8,10,[23][24][25].…”

“…Dvirnyi and Slyn'ko [23,24], constructing a piecewise differential Lyapunov function, established the stability of solutions to impulsive differential equations with impulsive action in the pseudo-linear form. Banks et al [8], using a Gronwall-type inequality and assuming that a matrix ( , ) satisfies a jointly Lipchitz inequality in and , established the robust exponential stability of evolution differential equations of pseudolinear form.…”

On the connected stability of the large-scale systems of dynamical equations on the time scale in critical cases

“…The modern achievements of the theory of the stability of the critical positions of equilibrium of ordinary differential equations include the establishment of the criteria of stability for model systems with a codimension of at most three inclusive, the establishment of the algebraic insolvability of the problem of the stability in the critical case [12], the study of the stability in resonance cases [12], the Molchanov's solution of the problem of the stability in the critical case of n pairs of purely imaginary roots in the absence of resonances [12,16], the study of the critical states of equilibrium of nonautonomous ordinary differential equations [20] and difference equations [10], the study of the critical positions of equilibrium of impulsive differential equations [5,8], and the proof of the semialgebraic solvability of the problem of the stability for monotone differential equations [15,17].…”